Abstract view
Exceptional Sets of Slices for Functions From the Bergman Space in the Ball


Published:20010601
Printed: Jun 2001
Abstract
Let $B_N$ be the unit ball in $\mathbb{C}^N$ and let $f$ be a function
holomorphic and $L^2$integrable in $B_N$. Denote by $E(B_N,f)$
the set of all slices of the form $\Pi =L\cap B_N$, where $L$ is a
complex onedimensional subspace of $\mathbb{C}^N$, for which $f_{\Pi}$
is not $L^2$integrable (with respect to the Lebesgue measure on $L$).
Call this set the exceptional set for $f$. We give a characterization
of exceptional sets which are closed in the natural topology of slices.